A balancing method for reduced order modelling of unstable systems

Moore's balancing method of model reduction has many attractive properties and is used widely in practice. However, this method suffers from the drawback that it is not applicable for unstable systems. This paper introduces a balancing method of model reduction to overcome this problem. The proposed technique obtains the reduced order model by balancing and truncating frequency domain controllability and observability Gramians. Analytical treatment is given for associated properties of the Gramians, and the balancing and truncation steps of model reduction. A numerical example is used to demonstrate the new approach.